Question on: JAMB Mathematics - 2019
Determine the values for which \(x^2 - 7x + 10 \leq 0\)
A
2 \(\leq\) x \(\geq\) 5
B
-2 \(\leq\) x \(\leq\) 3
C
-2 \(\leq\) x \(\geq\) 3
D
2 \(\leq\) x \(\leq\) 5
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Correct Option: D
\(x^2 - 7x + 10 \leq 0\)
Solving for \(x^2 - 7x + 10 = 0\), we have, (x - 5)(x - 2) \(\leq\) 0.
Given conditions:
case 1: (x - 5) \(\leq\) 0, (x - 2) \(\geq\) 0.
\(\implies\) x \(\leq\) 5; x \(\geq\) 2.
2 \(\leq\) x \(\leq\) 5.
Take x = 3,
3\(^2\) - 7(3) + 10 = 9 - 21 + 10
= -2 \(\leq\) 0.
\(\therefore\) 2 \(\leq\) x \(\leq\) 5.
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